Invariant imbedding analysis of seabed acoustics

The linear acoustic equations for the bounded slab of fluid ocean and elastic seabed with cylinderical symmetry are reduced to a set of coupled boundary value problems using separation of variables. In order to have a computational technique capable of handling stratification effects in the seabed, invariant imbedding is used to replace the boundary value problem with an initial value problem. As an initial approximation, the case of an ocean with a reflective bottom is considered and the change in the solution, as the depth of the seabed increases, is calculated. The method of invariant imbedding is shown to be numerically stable and has the advantage of assessing the effects of including an interactive seabed on the solution to the underwater acoustics problem with a reflecting seabed.